This paper proposes a conceptual and athematical framework that replaces the straight-line propagation of energy and fields, as traditionally assumed in quantum field theory (QFT), with a curved-wavefront perspective that aligns with the geometry of spacetime in general relativity (GR). By redefining straight beams as curved paths where the length of any beam equals the radius of a spherical wave-front at a given instant we achieve a unified description of energy propagation, reconciling wave-particle duality with spacetime curvature. This approachresolves inconsistencies between QFT and GR, offering a new lens for understanding phenomena like redshift, gravitational lensing, and wave-particle interactions in curved spacetime.

In this document, we fully review the theory and applications of the Eshelby Ellipsoidal Elastic Inclusion Problem. We rigorously derive all the equations related to the Eshelby Ellipsoidal Elastic Inclusion Problem and its applications to various Micro-mechanics problems like Ellipsodial Inhomogenity, Cracks, and Dislocations.

Although previous studies have established the predictive power of Lotka-Volterra models in financial markets, they assume static demand that does not account for exogenous factors or variable growth rates. The U.S. Domestic Airline industry, however, is an example of a dynamic market that is heavily reliant on customer demand and travel availability, which is why this study introduces non-autonomous models to accurately forecast future growth. Furthermore, only a few firms control most of the market share in this industry, and our study predicts Avelo Airline’s viability in direct competition with these larger, well-established airlines. Our approach not only studies the behavior of small companies in oligopoly markets, but also provides these firms with a framework to react to the growth rate of market- setters and determine the necessary growth to achieve long term viability in the industry. The model examines several methodologies for financial forecasting into one comprehensive model that enhances the predictive capabilities of Lotka-Volterra models, providing valuable insight for participating firms.

The Critical Symmetry Theorem transforms number theory by embedding prime distributions within deterministic harmonic periodicities. By enforcing symmetry, it aligns all non-trivial zeros of the Riemann zeta function (zeta(s)) on the critical line (Re)(s) = (0.5), resolving the Riemann Hypothesis. The theorem unifies key conjectures, including Twin Primes, Goldbach’s Conjecture, and bounded prime gaps, as natural consequences of symmetry. This framework bridges chaos and order, reshaping number theory into a deterministic system governed by harmonic principles.

In this report, I present the reflections from my colleague Abdelkader Sellal on the methods of representing the terrestrial gravity field and his proposals on the subject to encourage the young geodesists to discover these methods.

A technique for modeling plane wave propagation through inhomogeneous media and plasma layers with different electron densities is presented. The technique is based on transmission line theory. Therefore, a general technique is introduced for solving complex transmission line systems. A data structure and algorithm for representing, and simultaneously solving for all nodes within the transmission line network is presented. The method is based on representing the network as a recursive tree structure and solving for the voltage, current, and impedance at each node using recursive programming techniques. First, all frequency dependent parameters within the tree structure are updated, then in a post-order traversing of the tree, the impedance at each node are computed followed by a pre-order traversing of the tree to compute node voltagesand currents. For plane wave propagation, the reflection coefficient, the electric field andmagnetic field are computed. The method is applied to normal incidence but can easily be extended to oblique incidence. A tapered transmission line model was used to verify the algorithm. In addition, an example was provided verifying the ability to compute the frequency response and impulse response of a system with a plasma. Finally, the application of the technique to model the heat tile and the plasma that develops on either aero-assist or spacecraft re-entry is presented.This paper is based on work done at the Center for Communication and Signal Processing (CCSP) at North Carolina State University by the author in 1987. In addition, the paper presents work which was supported by NASA Langley Research Center under Contract NASI-1x925. The author was the Principal Investigator.

In special relativity, this paper presents four net forces, which can be applied in any massive or non-massive particle, and where the relationship between net force and special acceleration is as in Newton's second law (that is, the special acceleration of any massive or non-massive particle is always in the direction of the net force acting on the particle).

These are some notes on category theory that might be useful to a first-year graduate student in mathematics. This is the first of a three-part series including references to literature, on the theme of identity, examples of objects defined using the universal property and a section on monomorphisms and epimorphisms.

In this paper we investigate the legitimate and useful role of mathematics in science (and physics in particular). We also investigate the illegitimate and harmful role (or "lure") of mathematics in modern science (and theoretical physics in particular). Thanks to the obsession of contemporary scientists with complex mathematics and the wrong belief (as well as the wrong scientific values and standards) among these scientists that mathematics is the gold standard of excellent science, highly-mathematized and theoretized science (especially in modern physics) reaches these days a shocking level of irrationality and non-sensibility which often approaches the degree of delusion and hallucination. This obsession with complex mathematics and excessive theoretization inflicts serious damages to modern science and results in a huge waste of efforts and resources as well as the emergence of stray trends and bogus scientific theories inside and outside the main stream of science.

We study the Oxford Dictionary of English Christian Names by E. G. Withycombe, second edition. We draw the natural logarithm of the number of names, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,$beta H$=0) i.e. a magnetisation curve in the Bethe-Peierls approximation of the Ising Model with four nearest neighbours with $beta H=0$ i.e. in the absence of external magnetic field, $H=0$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature, H is external magnetic field and $k_{B}$ is the tiny Boltzmann constant.

This note formalizes and applies the emph{Principle of Structural Dependency}, which asserts that if the foundation of a mathematical structure ( B ) consists of another structure ( A ), then ( A ) cannot exhibit a property distinct from ( B ), while ( B ) may possess properties not shared by ( A ). We verify this principle and apply it systematically to reconstruct concise proofs of several classical theorems, including Cantor's theorem, the Fundamental Theorem of Algebra, the Jordan Curve Theorem, the Monotone Convergence Theorem, and the Pythagorean Theorem. These reconstructions emphasize the structural underpinnings of these results, offering a novel perspective and demonstrating how foundational relationships can simplify complicated proofs.

In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to partitions defined within the complex plane, which now serves as both the base and bearing set. We employ the expansion principles as central tools for rigorously investigating the possibility to partition numbers with base set as a certain subset of the complex plane.

In this paper, we study the map between problem and solution spaces. We introduce and develop a functional analysis on the topology of problems and their solution spaces. We introduce the notion of an textit{isotope} and corresponding textit{isotope} problem spaces and examine various notions compatible with this space.

A previously unknown relationship involving the masses of the neutron, proton, and electron is reported. Expressed simply, it states m_n/m_e = 2 Pi/ alpha (gamma - 1/gamma), where gamma is defined as (m_n - m_p)/m_e, and alpha = e^2/(2hc eps0) represents the fine structure constant. The accuracy of this approximation is 2.0 *10^-4, which is outside the experimental error of 4.0 *10^-6. Additionally, the coincidence gamma = log(4 Pi) holds, with an even closer match of 2.0 *10^-5, yet still outside the experimental precision of 10^-6.It is not claimed that these coincidences have a physical meaning.

Background: The Unified Theory of Multiversal Genesis (UTMG) proposes a novel cosmological paradigm where the universe emerges from the quantum vacuum through fluctuations of a unified field Φ. This process leads to the formationof multiple universes that interact via mechanisms mediated by strings and fields, resulting in a complex and interconnected multiverse.Methods: We developed a theoretical framework that unifies concepts from quantum mechanics, general relativity, and string theory. Detailed mathematical formulations describe the origin, evolution, and interaction of universes within amultidimensional bulk, employing advanced field equations and brane dynamics. Numerical simulations analyze the phenomena predicted by the theory, with justifications for the approximations used.Results: The UTMG provides equations governing the nucleation of branes from the quantum vacuum, iterative processes of universe multiplication through spontaneous symmetry breaking, and mechanisms of inter-universal interaction mediatedby open strings and the unified field Φ. The simulations support the theoreticalpredictions, showing brane formation and gravitational wave generation, with implications for observable signatures. Conclusions: The UTMG offers a coherent description of the genesis of themultiverse and inter-universal interactions, providing potential explanations to unresolved problems in cosmology. The theory’s predictions could be tested with future experiments and observations, opening new avenues for exploration in fundamental physics.

The international geodetic community lost, in December 2020, one of its eminent contemporary geodesists Professor E.W. Grafarend of the University of Stuttgart, Germany. To pay homage to him, I present to readers this article, it is a translation of one of his publications which appeared in The Canadian Surveyor, Vol. 28, No.5, December 1974, entitled "Optimization of Geodetic Networks".

In this paper, we present a novel series for approximating π that convergesrapidly. Each iteration produces three correct digits of π with only five terms,demonstrating a significant improvement in computational efficiency over exist-ing methods. We compare this series with traditional series such as the Gregory-Leibniz, Ramanujan, and Bailey-Borwein-Plouffe (BBP) formulas. Our analysisshows that the series is computationally simple while maintaining a rapid conver-gence rate, making it suitable for numerical applications requiring moderate preci-sion. We explore its potential use in both theoretical and applied mathematics.

We calculate the quantum corrections to synchrotron photon spectrum by methoddeveloped by Schwinger and Tsai. The traditional calculation method working withthe particle wave functions is here replaced by the mass operator approach avoidingthe particle final states and the integration over photon angular distribution. Thealgorithm of the calculation of the quantum corrections to the synchrotron radiationconsists in the evaluation of the forward Compton scattering process in the externalmagnetic field and then in application of the optical theorem to obtain the angularand frequency distribution.

This report presents the development and evaluation of a machinelearning model for identifying vulnerable C code. Using an AI-generateddataset of both vulnerable and non-vulnerable C code snippets, we explorevarious methodologies including Bag of Words (BOW), Logistic Regres-sion, word embeddings, and Recurrent Neural Networks (RNNs) to buildan effective classification model.

We propose a unified scalar field theory that modifies general relativity by intro-ducing a novel scalar boson coupling to matter, thereby altering the gravitationalinteraction at galactic and cosmological scales. The modified Einstein equations in-clude an additional term Φμν , representing the scalar field’s contribution to space-time curvature. This scalar boson, herein referred to as the Gravitational ScalarBoson (GSB), is hypothesized to possess a radially varying coupling strength α(r),enhancing its influence in regions where deviations from Newtonian gravity are ob-served, such as in galaxy rotation curves. We derive the theoretical foundationsof the model, discuss its implications for gravitational dynamics, and apply it tothe spiral galaxy NGC 3198 as a test case. The optimized coupling strength atr = 0, α0 = 0.254, aligns with theoretical expectations and complies with observa-tional constraints. Additionally, we explore the broader cosmological implications ofthe GSB, including its potential role in cosmic expansion and structure formation.Building upon this framework, we advance towards a unified theory by unifying allfundamental interactions and particles within this scalar field paradigm. Our resultssupport the potential of this unified scalar field theory, centered around the pro-posed GSB, as an alternative to dark matter in explaining galactic dynamics andoffer insights into a comprehensive unification of gravity with other fundamentalforces.

As shown in our publications, quantum theory based on a finite ring of characteristic $p$ (FQT) is more general than standard quantum theory (SQT) because the latter is a degenerate case of the former in the formal limit $ptoinfty$. One of the main differences between SQT and FQT is the following. In SQT, elementary objects are described by irreducible representations (IRs) of a symmetry algebra in which energies are either only positive or only negative and there are no IRs where there are states with different signs of energy. In the first case, objects are called particles, and in the second - antiparticles. As a consequence, in SQT it is possible to introduce conserved quantum numbers (electric charge, baryon number, etc.) so that particles and antiparticles differ in the signs of these numbers. However, in FQT, all IRs necessarily contain states with both signs of energy. The symmetry in FQT is higher than the symmetry in SQT because one IR in FQT splits into two IRs in SQT with positive and negative energies at $ptoinfty$. Consequently, most fundamental quantum theory will not contain the concepts of particle-antiparticle and additive quantum numbers. These concepts are only good approximations at present since at this stage of the universe the value $p$ is very large but it was not so large at earlier stages. The above properties of IRs in SQT and FQT have been discussed in our publications with detailed technical proofs. The purpose of this paper is to consider models where these properties can be derived in a much simpler way.

This paper builds upon https://vixra.org/abs/2402.0149 and https://vixra.org/abs/2406.0113, which proposed a novel realist framework for making sense of standard quantum theory. The framework is said to be ``realist'' in that it provides a complete observerless picture of quantum state ontology and dynamics, in conjunction with a mechanistic account of measurement processes, that answers basic questions of what, where, when, and how.The framework embodies a general quantum ontology consisting of two entities, called W-state and P-state, that respectively account for the wave- and particle-like aspects of quantum systems. W-state is a generalization of the wavefunction, but has ontic stature and is defined on the joint time-frequency domain. It constitutes a non-classical local reality, consisting of superpositions of quantum waves writ small. P-state is a non-local hidden variable that constrains the probability distributions governing deferred measurement outcomes, such as in the Einstein-Podolsky-Rosen (EPR) thought experiment. The framework features a full solution of the core measurement problem, which pertains to the global coordination within quantum systems required to bring about wavefunction collapse in causal fashion consistent with special relativity.The extent of development in those preceding papers amounts essentially to a quantum theory of matter particles. In this paper, it is shown how the realist quantum-theoretic framework for particles can be extended to encompass electromagnetic fields. The paper elaborates upon the implications for quantum gravity and how other interpretations (e.g., Many Worlds, GRW) deepen understanding of the realist framework.

The recent proliferation of so-called open-source large language models (such as LLaMA, Falcon, Mistral) has introduced a broader range of alternatives for AI practitioners and researchers. However, the majority of these models cannot be considered truly open-source, as they often provide only partial artifacts, such as final model weights or inference code. Furthermore, technical documentation accompanying these models tends to focus on high-level architectural decisions and superficial metrics, leaving critical aspects of the training process, including dataset composition, distribution, model checkpoints, and intermediate results, largely undisclosed. This lack of transparency presents a significant barrier to progress in the field, restricting the potential for open, collaborative research. In the absence of access to original datasets, attempts to further train or fine-tune these models by third parties are susceptible to issues such as catastrophic forgetting.In response to this challenge, we propose a method that facilitates more effective supervised fine-tuning of these closed-source models, without requiring access to the original data, while mitigating the risk of catastrophic forgetting.

We study the Santali head entries of two Santali to English dictionaries. These are Campbell's Santali-English Dictionary, third edition, edited by R. M. Macphail and A Santal Dictionary by Rev. P. O. Bodding, respectively.We draw the natural logarithm of the number of head entries, normalised(unnormalised), starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that Santali, the language of the Santal tribe, underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.

The discovery in 1998 that the universe is paradoxically accelerating its expansion has led some cosmologists to question the correctness of the non-Euclidean geometric theory of gravity, General Relativity. Physically assigning the term Dark Energy to the Cosmological Constant, sometimes viewed as a constant of integration, as the source of this acceleration has only produced even more questions. In the 17th century, there was also a great paradox between two views for the geometric constituents of a line, heterogeneous (made of points) versus homogeneous (made of infinitesimal segments). Evangelista Torricelli elucidated his logical reasoning on why lines must be made of infinitesimal segments instead of points and created one particular fundamental example among many. In this paper, I produce unknown corollaries to Torricelli's argument allowing me to falsify the relationship between his infinitesimals and the Archimedean axiom, resolve L'Hopital's paradox, as well as redefine the Fundamental Theorem of Calculus, scale factor/metrics, n-spheres and Gaussian curvature. I conjecture that the intractability of Dark Energy is due to the points of coordinate systems within General Relativity actually being a logically flawed heterogeneous interpretation. I propose that Euclidean and non-Euclidean geometry, and the physics equations based upon them, should be rewritten from the perspective of homogeneous infinitesimals. I introduce the geometrical logic in this paper in order to pave the way for the physical logic.

Using classical Doppler shift and wave mechanics, we derive a corrected equation for the fringe shift of the Michelson-Morley interferometer when rotated at an arbitrary angle in the presence of an aether wind, and demonstrate that the 1887 Michelson-Morley interferometer experiment can be interpreted as a positive detection of an aether wind of 235 km/s.

In this paper, we provide a detailed and rigorous proof that the series formed by the reciprocals of Sophie Germain primes and the series formed by the reciprocals of safe primes are both convergent. Utilizing analytic techniques and careful estimations of the counting functions for these primes, we establish upper bounds that demonstrate the convergence of these series.

This paper explores the extension of free electron behavior to general relativity through a closed algebraic Hamiltonian description of electron micro-oscillations. The author's research, which predicted the anomalous magnetic moment of electrons from first principles using closed algebraic equations, for a single electron oscillator, the time difference between rest and laboratory frames can be explained through the anomalous magnetic moment, providing a concrete mechanism for reconciling quantum and relativistic time concepts. The framework unifies seemingly disparate physical principles - energy conservation, geometric structure, and proper time - while offering an exact mathematical description of quantum phenomena that suggests a natural path toward bridging quantum mechanics and general relativity without requiring modifications to Einstein's theory. We present a detailed analysis of how an electron, when moving from point A to B, completely converts its mass energy into kinetic energy and subsequently reconverts it to mass energy at point B. Our analysis reveals that Snell's law governs these microscopic electron motions; this applicability of Snell's law naturally leads to the principle of least action, enabling us to demonstrate that electrons undergo micro-oscillations along geodesic paths. While conventional quantum theory, based on field theory, has struggled to reconcile its inherent absolute time with the relative time of relativity theory, our proposed 0-Sphere model represents individual quantum particles as micro-oscillators through closed algebraic equations. This enables the incorporation of both rest-frame and laboratory-frame time scales, as the model does not rely on the absolute time of field theory.

We present a novel method for learning hierarchical abstractions that prioritize competing objectives, leading to improved global expected rewards. Our approach employs a secondary rewarding agent with multiple scalar outputs, each associated with a distinct level of abstraction. The traditional agent then learns to maximize these outputs in a hierarchical manner, conditioning each level on the maximization of the preceding level. We derive an equation that orders these scalar values and the global reward by priority, inducing a hierarchy of needs that informs goal formation. Experimental results on the Pendulum v1 environment demonstrate superior performance compared to a baseline implementation.We achieved state of the art results.

The aim of this article is to prove that all the roots of the Dirichlet eta function are only on the critical line, which implies that the Riemann hypothesis is true. The roots of the eta and zeta functions in the critical strip are the same. We shall investigate the possibility or not of existence of roots of the eta function which are in the critical strip and not on the critical line.

This hypothesis views the universe as a dynamic structure that was formed not by a single, all-encompassing Big Bang, but through several independent cosmic energy bursts cite{penrose2010cycles, steinhardt2002colliding}. Such events could have occurred over very long periods in various regions of a possibly unbounded cosmic space, where universes expand freely without separating membranes or isolating structures. The aim of this hypothesis is not to challenge the Big Bang theory but to broaden it with a more comprehensive perspective. While the classical Big Bang theory provides us with the image of a singular origin, this hypothesis suggests that various cosmic events may have contributed jointly to the formation and structuring of the universe.

In this paper we show that area of any quadrilateral can be estimated from the four lengths sides. With the Triangle Inequality Theorem and a novel provided diagonal's formula, the boundaries of quadrilateral diagonals are found. Finally Bretschneider's formula can be applied to find a set of possible areas.

In this paper of "The Epistemology of Contemporary Physics" series we investigate Newton's third law and discuss and analyze its epistemological significance from some aspects with special attention to its relation to the principle of conservation of linear and angular momentum. The main issue in this investigation is the potential violations of this law according to the claims made in the literature of mainstream physics. This issue may cast a shadow on the validity of classical mechanics, and its Newtonian formulation in particular, formally and epistemologically and could have important implications and consequences on contemporary physics in general. However, what is more important about this issue from our perspective is the lack of clarity, comprehensibility and coherence in the investigation and analysis of this issue and its implications marked by the absence of appropriate conceptual and epistemological frameworks to deal with this issue properly and systematically. As a result, what we find in the literature is a collection of contradicting views which are mostly based on personal choices and preferences and selective or biased theoretical analysis with the lack of proper experimental verification and substantiation.

Generative AI models are increasingly used across various modalities, including text, images, audio, and video. Estimating the computational cost of generating con- tent is crucial for optimizing performance and resource allocation. This paper intro- duces the Cost-Per-Byte Principle: C = T × I, a universal law that relates the cost of content generation to per-byte generation time and per-second inference cost. We derive the per-byte generation time analytically based on the model’s computational requirements (FLOPs) and the hardware’s performance (FLOPs per second). By estab- lishing mappings between bytes and different content units (characters, pixels, samples, frames), we provide a modality-agnostic framework for cost estimation. We present a rigorous proof of the principle’s validity and apply it to estimate the costs of current popular models, using publicly available evidence to verify the accuracy and usefulness of this principle.

In this paper we will prove that if a compact $A$ in $R^n$ belongs to the unit ball in $R^n$, then $A$ has a slice of measure greater than a calculable constant times the measure of $A$. Our result is sharp.

It is shown that the limit of cos(j) and sin(j) as j goes to infinity do not exist. Using DeMoivre's theorem this implies the limits of sin(j!) and cos(j!) don't exist either. Assuming pi is rational, its multiple can be expressed as a factorial. From this a contradiction is derived.

The value of the gravitational wave energy density is unknown. Current progress in gravitational wave detection suggests that the energy density of the stochastic gravitational wave background (SGWB) will be estimated in the next decades. We present a derivation of its value under the assumption that energy lost due to cosmic redshift is fully responsible for the energy gained by the cosmological constant in the expanding universe. This unknown non-local mechanism of energy conservation on the cosmic scale could explain dark energy and hint at a property of a theory of quantum gravity.

A non-singular black hole solution is briefly presented which violates energy conditions only at its interior by postulating a consistent shift to negative energies and gravitationally repulsive negative masses at the event horizon. This shift is the unitary parity-time $PT$ transformation of relativistic quantum mechanics and the proper antichronous transformation of the full Lorentz group. The transformation at the event horizon respects Einstein's equivalence principle, and the considered negative mass interaction does not result in the runaway motion paradox or vacuum instability. The correspondence of these regular black holes with observed ones is studied by proposing another mechanism of black hole growth independent of accretion and merging due to interior increasing entropy, which attempts to solve the unexplained size and formation of high-redshift supermassive black holes, the intermediate mass gap, and the information paradox.

Milgrom's Modified Newtonian Dynamics (MOND) correction to Newtonian gravity is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach's principle. Both Newton's gravitational constant and Milgrom's MOND acceleration parameter or scale constant are substituted for the speed of light and two varying and measurable cosmological parameters under the justification of Schrödinger's and Sciama's interpretation of Mach's principle: causally connected mass and size of the universe. This Machian interpretation, free from fundamental constants and free parameters with the exception of the speed of light as the speed of causality and gravity, is based on relative field intensities of the small and large scale of the universe. The Machian MOND approximation is a necessary feature of a phenomenological theory of modified inertia which incorporates Mach's principle in agreement with galaxy rotation curves.

This article addresses several key issues with the current laws of electrodynamics, including Lorentz’s law, Faraday’s law, and the Maxwell-Ampere law, by highlighting various scenarios where these laws fail to describe physical phenomena. It also presents a case where the condition div{B}=non-zero occurs, challenging the standard belief that magnetic fields always have zero divergence. The article argues that magnetic fields, as traditionally understood, do not actually exist. Instead, effects thought to be caused by magnetic fields are simply due to electric fields (no need to include special theory of relativity). A new concept introduced in the article is the "drag property of the electric field," a previously unknown characteristic that creates the illusion of a magnetic field. Using this drag property, the article derives a set of revised electrodynamic laws that consistently apply across all situations. Additionally, it addresses the failure of the traditional atomic model and suggests a new approach. The article also challenges the idea that space is empty, proposing that space is filled with something rather than being a true vacuum. This research offers a fresh perspective on both electromagnetic theory and the nature of space.

In this paper, we will expose for the Gaussian multiple causation a theorem relating the causation to correlations.This theorem is based on another equality which will be also proven.

We present Vibrational Field Dynamics (VFD), a novel theoretical framework that introduces a fundamental resonance structure to spacetime and field interactions. The theory extends the stan-dard model and general relativity through a unified mathematical formalism characterized by resonance functions Rh(ω), which naturally emerge from the theory’s core principles. VFD addresses several outstanding problems in theoretical physics, including quantum gravity unification, dark sector dynamics, and the information paradox in black hole physics. The framework introduces modifications to quantum field theory and gravitational interactions through a resonance based coupling mechanism, leading to specific, experimentally testablepredictions. We derive modified field equations that reduce to known physics in appropriate limits while providing new insights into high energy phenomena, cosmological evolution, and quantum-gravitational effects. Key predictions include modifications to gravitational wavesignatures, quantum interference patterns, and dark sector interactions, all parameterized by experimentally accessible coupling constants. The theory’s mathematical structure maintains consistency with existing observational constraints while offering novel explanations for current anomalies in cosmological and high-energy physics data.

The Riemann Hypothesis remains one of the most critical unsolved problems in mathematics, proposing that all non-trivial zeros of the Riemann zeta function are located on the critical line. This paper explores unique fractal structures within the zeta function, drawing comparisons with the Mandelbrot set and the Smith chart, which together illuminate possible connections between prime distribution,electromagnetic symmetry, and gravitational principles.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. It is also a powerful tool for analysis. This article studies the symmetry of the coefficients in Formal Calculation. Three types of extended numbers were introduced, and many formulas for symmetric functions were obtained.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained many results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry

This paper introduces a novel cosmological framework that interprets the vacuum as a dynamicsystem of harmonic oscillators, expanding at relativistic velocities and interacting with an antimatteranti-universe. By modeling the vacuum as an RLC circuit, it is proposed that the vacuum itselfbehaves as a resonant system of harmonic oscillators. Within this framework, they are derivednew relationships between fundamental constants—including the speed of light c, gravitationalconstant G, and fine-structure constant α— showing that these constants arise from the vacuum’sintrinsic properties and oscillatory dynamics.Based on the relationships derived within this framework, it is proposed a novel mechanism ofenergy exchange across the boundary between matter and antimatter domains, through quantumgaps conceptualized as a "Quantum "black" hole" network. These "holes" in the boundary facilitateenergy transfer, generating local spacetime deformations that we perceive as gravitationaland electromagnetic interactions. It is showed that spacetime curvature and force interactions areemergent phenomena, stemming from quantum fluctuations within the vacuum as it oscillates andexpands. By reinterpreting the vacuum as an active, resonant medium, it is offered a cohesiveframework that may unify quantum mechanics and general relativity while aligning with observedcosmological expansion.

While the original Born-Infeld model describes electrons as solutions of classical field equations, there are also several classical particle models that describe electrons as point-like particles. Along the lines of research on these models, the present work proposes a new model of point-like electrons, which represents the peak of a rotating field solution of a modified Born-Infeld field theory by a relativistic, point-like particle. This new model is compared with a recently published neo-classical model of point-like electrons in order to clarify similarities and differences.

Physical reality is here framed as the necessary geometric consequence of endowed energy release from a single zeroth-dimensional oscillator, which exists as the requisite conserving balance point for projection of the entire universe. The framework requires exactly one parameter - the initial oscillator energy - from which all physical constants, forces, and dimensional structure emerge through required quadratic self-reference and phase coherence preservation. All constants of the standard model are herein geometrically given. The fundamental nature of time is revealed as the oscillator's required principal orthogonal eigenvector. The necessary condition for the existence of reality is developed. Observed energy ratios are revealed as inherent. Feynman's infinities are resolved. Experimental predictions testable through phase-coherent optical interference patterns are given with precise energy ratios derivable from geometric constraints. Theory of mind is proposed as the minimum sufficient phase coherent structure required to form a self-representation of the oscillator. Remarkable analyses of coherent group consciousness are revealed. Reality itself, including conscious observation and intention, manifests as the inescapable geometric realization of the oscillator's self-referential structure.

The most popular approach of understanding the cosmic evolution is Einstein’s General Relativity(GR). GR is the classical gateway to obtain the dynamics of the cosmic fluid and it canat best describe the macroscopic evolution of the Universe. In this work, we have accomplishedan alternative tool to examine the microscopic dynamics of the cosmic fluid particles via quantumfield theory (QFT). We have proposed a cosmic fluid model with complex scalar field Lagrangiancorresponding to the modified Klein-Gordon equation (KG equation) of the scalar field in FLRWspace-time. Following this Lagrangian, the cosmic fluid system has been quantized under certainrestrictions on the parameters. This restrictions are used to determine the cosmic evolution patternin the macroscopic level.

In this paper a theorem will be proven that is a relatively concise way to confirm the irrationality of an infinite series. From this, new proofs of the irrationality of some known results can be derived(pi, phi) as well as solutions to open problems(rationality of zeta function over the natural numbers, rationality of Euler-Mascheroni Constant)

The increasing incorporation of speculative constructs such as dark matter, the Higgs field, and cosmic inflation within modern physics indicates a shift towards metaphysical frameworks, potentially compromising the empirical rigor traditionally upheld in physical sciences. This article critically evaluates the foundational paradigms in quantum mechanics and cosmology, asserting that constructs like the Big Bang theory and baryogenesis introduce elements that lack experimental validation and challenge established physical principles. By examining the epistemic and methodological implications of these paradigms, the author argues that theoretical physics must resist the encroachment of metaphysical assumptions and prioritize models grounded in measurable, observable phenomena. The article proposes a recalibration of the discipline, advocating for a return to empirically verifiable principles and logically cohesive theories that align with classical physics. Through this approach, theauthor suggests, physics can maintain its empirical integrity, ensuring that theoretical advancements remain anchored in experimentally testable reality and do not drift into speculative abstraction.

In this note, we introduce and develop the analysis of the fractional invariance. This analysis is used for estimating the partial sums of arithmetic functions $f:mathbb{N}longrightarrow mathbb{R}$ of the form $sum limits_{substack{nleq xin mathbb{A}}}f(n)$ for $mathbb{A}subseteq mathbb{N}$. This analysis can be applied to a broad class of arithmetic functions.

In this paper, we present an integral representation involving trigonometric functions and variable transformation techniques to turn it into a triple integral. The proposed integral is initially simplified using trigonometric identities, so we rewrite the original integral in terms of a three-variable integral representation. The main theorem demonstrates the equivalence between the initial integral and the resulting triple integral, illustrating the applicability of trigonometric identities in calculations of complicated integrals.

In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian formulations. As we will see, none of these formulations provide a clear and consistent framework for understanding the physics which they represent and hence they all represent valid formalism without proper epistemology or sensible interpretation.

This paper presents a novel perspective on the nature of space and time, arguing for the coexistence of both absolute and relative aspects at the classical level and the existence of only absolute aspects at the quantum level. We propose using various arguments that the static space-in-itself exists as absolute space and the universal objective present moment with an infinitesimal duration continuously exists as absolute time in the universe since its creation until the present, along with the measured space being relative space and the measured time being relative time. We also prove the continuous nature of absolute and relative space, absolute and relative time, and relative spacetime and, thus, challenge all theories that use discrete relative space or discrete relative time or discrete relative spacetime, such as loop quantum gravity and causal set theory, among others. This framework dissolves several fundamental problems: the quantum gravity question by proving its impossibility due to the absence of reference frames at quantum scales, the unified field theory question by proving its impossibility by showing gravity’s classical-only nature, whereas electromagnetic force being present at quantum and classical level both, and the wave-particle duality through establishing universal quantum fields/waves as the sole quantum reality with each of these fields being one singular reality with varying level of intensity at different spatial regions in the universe and with continuous non-deterministic interactions explaining quantum phenomena without randomness while preserving causality and particles being just the 1emergent reality at the classical level. We also disprove string theory and any potential higher spatial dimensional theory using fundamental logic. Thus, this comprehensive framework completes Einstein’s unfinished revolution in understanding space, time, and physical reality at both quantum and classical levels.

The application of deep neural networks in geospatial data has become a trending research problem in the present day. A significant amount of statistical research has already been introduced, such as generalized least square optimization by incorporating spatial variance-covariance matrix, considering basis functions in the input nodes of the neural networks, and so on. However, for lattice data, there is no available literature about the utilization of asymptotic analysis of neural networks in regression for spatial data. This article proposes a consistent localized two-layer deep neural network-based regression for spatial data. We have proved the consistency of this deep neural network for bounded and unbounded spatial domains under a fixed sampling design of mixed-increasing spatial regions. We have proved that its asymptotic convergence rate is faster than that of cite{zhan2024neural}'s neural network and an improved generalization of cite{shen2023asymptotic}'s neural network structure. We empirically observe the rate of convergence of discrepancy measures between the empirical probability distribution of observed and predicted data, which will become faster for a less smooth spatial surface. We have applied our asymptotic analysis of deep neural networks to the estimation of the monthly average temperature of major cities in the USA from its satellite image. This application is an effective showcase of non-linear spatial regression. We demonstrate our methodology with simulated lattice data in various scenarios.

This short document purported to publicise assorted constants to be targeted for Reverse Arithmetic (known as unscrambling the egg in pop culture) experimentation. In section one, a tangential intermezzo intended to justify the urgency to archive and some trivia regarding Pie and its defense against the manifesto of otherwise obscure alternative. Later sections detail the constants aimed for Reverse Arithmetic experimentation.

In this paper, we investigate the interaction of two breathers in the Sine-Gordon model. We derive an explicit analytic expression for the two-breather solution of the Sine-Gordon equation and study its dynamics. We show that the breathers behave like classical particles of equal masses upon collision, but with the momentum continuously transferred via their fields. By suitably averaging the oscillations of the solution we derive analytic expressions for the trajectories of the two breathers. It is shown that in the non-relativistic limit, the interaction potential between the two breathers has the same form as the velocity-dependent interaction potentials used for Machian unified theories of gravity and inerita.

The article presents a relativistic extension of Newton's second law of motion, adapted to a four-dimensional spacetime construct where time and space are treated under the framework of special relativity. By introducing a unique concept of"U-space", where time functions as a spatial coordinate with its own metric pro-perties, the study explores Newtonian dynamics through a relativistic lens. Thisexploration includes the derivation of relativistic force and acceleration equations,considering both constant and variable rest mass scenarios. The derived formulations, based on the principles of special relativity, are presented with modications that incorporate mass-energy equivalence, enabling a more comprehensive understanding of force interactions within relativistic contexts.

Textbooks tell us that the coupling constant of Dirac magnetic monopoles is 34.259. Here I show by using the quark hypothesis that at zero temperature the coupling constant is as high as 308.331. Moreover I show that it is a running coupling constant and is smaller than 0.5 at the Planck temperature.

We consider the possibility that black-body photons are created by the energetical sources in space. It leads to the integral equation for the energy distribution of sources. The Planck formula for photons is, in this situation, valid, for the special distribution of sources. It means that the black-body is at the crystalline form.

In this article, study related to the distribution of the Goldbach prime pairs for the even integers of form 2(n+1)^{2} has been carried out with the help of other conjectures(/postulate), that is, Legendre's conjecture and Bertrand's postulate. From the obtained results, various possible conjectures have been proposed/suggested. In brief, first the term, Goldbach first prime pair (p_{f},p'_{f}) was defined and for ascertaining the interval in which Goldbach first prime pair would always be present for all the values of 2(n+1)^{2}, where, n =1,2,3,..., was suggested. The proposed conjectures on distribution were tested for all values of n = 1,2,3,...,1,000,000 using algorithm. The expression, (n)(n+1) < p_{f} < (n+1)^{2} < p'_{f} < 2(n+1)^{2} - n(n+1) showed that, the Goldbach first prime pair would always existing for all the n values, where, n = 1,2,3,...- {4,6,10,16,19,21,22,23,30,33,36,43,48,49,56, 57,61,66,72, 76,81,106, 117,127,130, 132,141,210,276,289,333,418}. The expression, (n)^{2} < p_{f} < (n+1)^{2} < p'_{f} < 2(n+1)^{2} - (n)^{2} showed that, the Goldbach first prime pairs would always existing for all the n values, where, n = 1,2,3,... - {21,23,30,33,36,48,49,117,141}. While, for the expression, (n)(n-1) < p_{f} < (n+1)^{2} < p'_{f} < 2(n+1)^{2} - (n)(n-1), were true for all the n = 1,2,3,..., values. Another observation was found that, in the proposed conjecture 1, the gap between Goldbach first prime pair, that is, (p'_{f} - p_{f}) was found to be always less than its corresponding n value after n=2538 , hence, Gap(p'_{f} - p_{f}) << n, where, n=2539,2540,2541,....

We integrate the nonlinear Schrödinger differential equation, looking for "lone wave" solutions, and then use the method ofindeterminate coefficients.The integration is in closed form for the free particle, and then we integrate numerically for the particle subject to a weak periodic potential. In both cases, the system is one-dimensional.

This document proves that the Collatz Conjecture is true for the Natural numbers excluding zero. Use is made of the probability distribution of even and odd numbers in supposed diverging Collatz sequences to establish that Collatz sequences do not diverge, having a finite number of terms, and are bounded. Finally proof by contradiction, the pigeon hole principle and proof by induction are used to prove that the Collatz Conjecture is true via two theorems.

This paper examines the relationship between interest payments as a percentage ofgovernment revenue and the stability of reserve currencies, identifying critical thresh-olds that historically preceded currency crises or the loss of reserve currency status.Through detailed analysis of cases including the British pound sterling, Argentine peso,Greek drachma, and Japanese yen, we identify a consistent pattern where fiscal crisesemerge when interest payments reach 20-30% of government revenue. This thresh-old appears remarkably stable across different historical periods, economic systems,and levels of development. These findings have profound implications for the UnitedStates, where interest payments are projected to rise from 19.5% of revenue in 2024to 63.4% by 2028, far exceeding historical crisis levels. The paper analyzes both do-mestic challenges (including demographic pressures, political gridlock, and structuraleconomic issues) and international pressures (such as de-dollarization initiatives, dig-ital currency development, and changing geopolitical dynamics) that could acceleratea potential crisis. We examine potential policy responses across fiscal, monetary, andstructural domains, while acknowledging the significant political and practical chal-lenges to implementation. The analysis suggests that the convergence of these factorscreates an unprecedented risk to dollar stability, potentially requiring preventive actionbefore critical thresholds are breached to avoid a disorderly adjustment in the globalmonetary system.

Qualia—the subjective experience of perception—has long been considered unique to biological consciousness. However, with the advent of sophisticated Artificial Intelligence (AI) models, the question arises: could complex AI architectures also manifest a form of qualia, albeit different in nature from biological systems? This paper explores the hypothesis that both biological and artificial systems may generate unique moments of consciousness or qualia through information processing. By examining theories of consciousness, such as emergentism and Integrated Information Theory (IIT), this paper discusses the potential for qualia to arise as an emergent phenomenon in systems that handle complex information processing. Additionally, the ethical implications of AI-generated qualia are explored, alongside a discussion of what this means for the future of AI and philosophy of mind.

This article investigates the two-dimensional Brouwer Fixed-Point Theorem within the context of a surjective continuous transformation function ( f(x) ). This function can be interpreted as defining a continuous vector field. In this framework, each point in the disk is mapped to another point via a specific vector associated with the continuous transformation, thereby establishing a coherent vector field. This function can be interpreted as defining a continuous vector field. In this framework, the vector field can be decomposed two vector fields. Instead of  proving the existence of fixed point directly, the article aim to focus on prove the vector fields always has intersection where at this point, the vector fields has opposite directiond and same norm.The paper also provide the programming experiment which further verifies the proof.

This article present a constructive proof by analyzing decompositions of continuous vector field. The original proof of Brouwer's theorem relies on a contradiction argument, which, while effective, does not offer a constructive method for locating the fixed point. Through projecting arbitrary vector field the basis of the vector field, it can be proved there exists zero points on both of the basis. The article will also generalize the proof from 2D to 3D dimensions. The method is also valid under surjective and scaling map.

Despite decades of research, the origin of high-temperature superconductivity is still unclear, and its microscopic mechanism remains a subject of intense debate. The intrinsic Mott insulating properties of copper oxide parent compounds and the experimentally observed charge-ordered phases in real space suggest that high-temperature superconductivity may stem from localized electrons rather than itinerant electrons. In this work, we propose a unified microscopic mechanism where confined electrons within polyhedral quantum wells represent the Mott ground state, and symmetry-breaking of electron-hole pairs acts as the superconducting mechanism. A single parameter formula for the critical temperature (Tc) of unconventional superconductors is developed, allowing accurate determination of Tc based on lattice constants. The approach elucidates relationships between various charge-order phases and doping concentration, explores Fermi surface structures, investigates spin resonance peaks and parities, and examines pressure-induced dual superconducting phase transitions - all consistent with experimental observations. It is also estimated that the highest Tc of the newly discovered nickel-based superconductor will not exceed 100 K. This work offers critical insights into unconventional superconductivity’s fundamental mechanisms while introducing a new paradigm to reveal more intrinsic connections between superconductivity, conductivity, and magnetism.

Chord diagrams are cubic graphs with two types of edges: the first set of edges comprise a subgraph which is a simple cycle (the frame); the second type of edges (the chords) comprise disconnected 2-vertex subgraphs incident to distinct vertices of the frame. We define associated cubic graphs with directed chords (arcs) while keeping the edges of the frame undirected, and plot all 1, 3, 13, and 121 of them for 2, 4, 6, and 8 vertices.

A very important concept for the evolution of a wonderful world, the "goodness" having survived to the "evilness" should be isolated , industrially grown, stimulated for a further evolution and finally released. Another important concept, Herpesviruses infecting human neural cells would enforce a large human brain diversity. A wonderful world could be built from a golden balance between the two concepts mentioned previously.

Physical phenomena, sometimes with the exception of gravity, are usually assumed to be described by Lorentz transformation covariant theories, and the validity of the Lorentz transformation has been empirically verified to very high accuracy. The Einstein equation of gravity theory, however, has an infinite set of metric solutions, an infinite subset of which aren't Lorentz covariant, and one of the latter might be taken as valid, e.g., the Robertson-Walker metric for cosmology. But if all of nongravitational physics is in fact Lorentz covariant, it would almost certainly be physically inconsistent for gravity theory not to be Lorentz covariant as well. The solution ambiguity of the Einstein equation is a consequence of its important symmetry of general coordinate transformation covariance. However the four-vector potential form of electromagnetic theory has an analogous solution ambiguity as a consequence of its important symmetry of gauge transformation invariance, but in that case it is standard practice to break this symmetry by imposing the retarded Lorentz gauge condition, the simplest gauge condition which is Lorentz covariant and causal. Here we show that both gauge transformation invariance in electromagnetic theory and general coordinate transformation covariance in gravity theory arise spontaneously from fully Lorentz covariant initial assumptions. These subsidiary dynamic symmetries crucially affect the structure of the equations of their respective theories, but any solutions they happen to admit which aren't fully Lorentz covariant are ipso facto excluded by the fully Lorentz covariant initial assumptions.

In this article, we present novel additive properties for the g-Drazin inverse within the context of Banach algebras. Subsequently, we provide representations for the g-Drazin inverse of block operator matrices defined over Banach spaces. These findings build upon and extend various well-known results, such as those by Bu, Feng, and Bai (J. Comput. Appl. Math., 218(2012), 10226--10237) and Dopazo and Martínez-Serrano (Linear Algebra Appl., 432(2010), 1896--1904).

We develop the analysis of the theory of problem and their solution spaces. We adapt some classical concepts in functional analysis to study problems and their corresponding solution spaces. We introduce the notion of compactness, density, convexity, boundedness, amenability and the interior. We examine the overall interplay among these concepts in theory.

A continuation of the Born Reciprocal Relativity Theory (BRRT) program in phase space shows that a natural temperature-dependence of mass occurs after recurring to the Fulling-Davies-Unruh effect. The temperature dependence of the mass $ m ( T ) $ resemblances the energy-scale dependence of mass and other physical parameters in the renormalization (group) program of QFT. It is found in a special case that the effective photon mass is no longer zero, which may have far reaching consequences in the resolution of the dark matter problem. The Fulling-Davies-Unruh effect in a $ D = 1 + 1$-dim spacetime is analyzed entirely from the perspective of BRRT, and we explain how it may be interpreted in terms of a linear superposition of an infinite number of states resulting from the action of the group $ U (1,1) $ on the Lorentz non-invariant vacuum $ | {tilde 0 } angle$ of the relativistic oscillator studied by Bars cite{Bars}.

The present article provides a detailed mathematical treatise on the geometry of skateboard transition ramps. These usually form a circular segment shape and are used in skateboarding for transitioning from a horizontal plane to another angle of incline. Transitions play a crucial role in the flow of skateparks and are required, for example, for quarter pipes, mini ramps, vert ramps, or jump ramps. Skateboarding has been an Olympic sport since 2023, yet many publicly funded skateparks still do not meet the demands of the sport. On one hand, there is often a lack of willingness from authorities to engage with the athletes beforehand; on the other hand, the people involved in the planning process often lack the necessary experience and mathematical expertise to perfectly fulfill the users' needs. Thoughtful planning is particularly crucial for ramps with curved surfaces to ensure the flow of the skatepark. In addition to the mathematical analysis, source codes for programs are provided to make the calculations as convenient as possible for all users.

In this study, we analyze a dataset of survey papers on Large Language Models (LLMs) published over the last 3 years to gain insights into the current trends surrounding LLMs. Primarily we analyze the author landscape and the effectiveness at predicting the taxonomies of the surveys from their title, summary, and listed categories. I find that the amount of surveys released has increased drastically in the last three years. Also, most surveys have around 8 authors, but each author appears only on one survey usually. This indicates the research is spread widely between those in the field. Finally, our investigation into predicting taxonomies was a failure with the machine learning methods we applied. However, valuable insights about the dataset can be gained from the attempts.

In this paper, we investigate the p-Drazin inverse of the anti-triangular operator matrix $left(begin{array}{cc} a & 1 b & 0 end{array} ight)$. We identify two new class of necessary and sufficient conditions for an anti-triangular matrix to possess a p-Drazin inverse. Subsequently, we generalize several established results to a broader context. As practical applications, we demonstrate the p-Drazin invertibility of specific block operator matrices $left( begin{array}{cc} A & B C & D end{array}ight)in mathcal{B}(Xoplus X)$.

It is known that the equation X^4+Y^-(Z^4+W^4) = N has infinitely many rational solutions for any rational number N.We present three new solutions for the equation X^4+Y^4-(Z^4+W^4) = N.

Two essential conceptual structures - impedance quantization and geometric representation of Clifford algebra - were lost in physics. Background independent analysis of Mach’s principle makes possible calculation of quantum impedance networks of wavefunction interactions in the background independent geometric representation. Their synthesis fills gaps in the history of physics.

In this note, we give the details of how to calculate the parameters of the transformation from STT or local coordinate system to the NTT coordinate system the Tunisian geodetic terrestrial system.

We study the head words of the Thai-English Student's Dictionary compiled by Mary R. Haas,way back in 1964.We draw the natural logarithm of thenumber of head words, normalised, starting with a letter vs the natural logarithm of therank of the letter, normalised.We conclude that the Dictionary can be characterised by BP(4,$beta H=0$), themagnetisation curve for the Bethe-Peierls approximation of the Ising model with four nearest neighbours in the absence of external magnetic field.$beta$ is $frac{1}{k_{B}T}$ where, T is temperature, H is external magnetic field and$k_{B}$ is the tiny Boltzmann constant.

We analyze intervals of numbers whose prime factors are all $> y$. In this article we stablish and prove a lower bound of prime numbers contained in the interval $[x^a,(x+1)^a)$ where $a,x in mathbb{R}^+$ and $x>2$, $a geq 2$, then if $a=2$, the interval $[x^2,(x+1)^2)$ contains at least 1 prime.

In this paper we prove the fundamental contradiction about the Riemann Hypothesis, expressing a function as a product and given the following summation, where $R$ is the set of all solutions of $R(x)=0$:begin{equation}frac{R'(x)}{R(x)}=sum_{rin R}left(frac{1}{x-r}ight)end{equation}And considering a regularization for hypertranscendental functions, then the expression applied in Riemann Zeta function of $frac{1}{2}$, or the logarithmic derivative, where $R_t$ is the set of tirivial zeros:begin{equation}frac{zeta'(frac{1}{2})}{zeta(frac{1}{2})}eq sum_{rin R_t}left(frac{1}{frac{1}{2}-r}ight)end{equation}

This preprint article proposes an unconventional topological fields model based on two interacting fields that form a non-formal octonionic, bilateral structure.Within this framework, nuclear interactions unfold through a complex time dimension that combines real past and imaginary future components, facilitating mass and energy exchanges between protons and antineutrinos or antiprotons and neutrinos during beta decay reactions. The neutron is reinterpreted as a transitional state in transformations between proton and neutrino and antineutrino and antiproton, or vice versa.This octonionic configuration, with six spatial imaginary hyperdimensions, one imaginary time hyperdimension, and one real time dimension, brings highly abstract and advanced algebraic concepts to life through a concrete physical mechanism, offering a natural unification of the weak, strong, and electromagnetic atomic interactions.Moreover, the octonionic approach provides a geometric interpretation of Quantum Chromodynamics (QCD), clarifying the internal structure and relationships between quarks and gluons.

This paper presents a mathematical framework for integrating tensor fields with angular components, combining linear and angular integrands to form a comprehensive expression. We focus on the integration over spatial variable ( x_i ) and angular variable ( theta ), deriving a combined integrand that reflects the interplay between these dimensions. The methods are implemented computationally, and the resulting combined integrand is visualized to provide insights into its behavior.

We present a formal mechanical analysis using sweeping net methods to approximate surfacingsingularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stabilityof the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

In this paper, we show that many well-known chaotic maps can be generated by discretizing the equations of memristor or nonlinear resistor circuits using the Euler method or the central difference method.These examples show that the dynamics of a wide variety of nonlinear maps, such as those found in engineering, physics, chemistry, biology, and ecological systems, are closely related to the discretized memristor or nonlinear resistor circuit equations. Furthermore, the discretized memristor circuit equations also propose the new modified or simplified version of the well-known chaotic maps. We also propose the generalized extended memristor with non-volatility property. To satisfy the non-volatility property, the $v-i$ characteristic of the generalized extended memristor is defined by two bounded functions, namely the resistive-fuse function and the saturation function. Using this element, the discretized two-element memristor circuits can generate any two-dimensional chaotic map. The computer simulations in this paper show that the discretization of the memristor or nonlinear resistor circuit equations is one of the most promising methods to find interesting chaotic maps. Furthermore, some of the discretized three-dimensional circuit equations clearly show the topological structure of the chaotic attractors.

I would like to talk about the falsity of the theory of relativity. I understand that shouts will now begin: "How long is it possible? Alternatives again." I'll answer this. Let's argue. Just argue without insults. Those who protect Einstein, as a rule, does not provide any evidence and only call names. And their main argument: "You are a fool!" Of course, you can't argue with this. Well, seriously, let's figure it out. Critics of the theory of relativity have appeared since its inception. There has never been such a period in recent history of science when there were no critics of Einstein. Doesn't this worry anyone?! Why are there no critics of Newton and the classical mechanics and mathematical analysis he created?! Not everyone even knows why Einstein received the Nobel Prize. Many people think what kind of theory of relativity. In fact, this is not true. Einstein was given a prize for explaining the two laws of the photoelectric effect. At the same time, the Russian scientist Stoletov made a significant contribution to the research of the photoelectric effect. But in the West they prefer this don't remember. This is understandable. They rarely give Nobel Prizes to Russians. It should be noted that at first no one took the theory of relativity seriously. When Einstein was given Nobel Prize, it was said that the prize was awarded despite the dubiousness of his other theories and the presence serious objections to them. I will not list all the contradictions here. Simply because the number of given the arguments are unlikely to convince the most notorious skeptics.

Space exploration is a primary goal for leading companies in the aerospace market. One of the major challenges in this environment is the high intensity of space radiation, which poses a serious threat to both human health and spacecraft instrumentation. For instance, while humans can only tolerate up to 4 Sv of radiation, exposure in space can reach 12 Sv. The main sources of this radiation are solar emissions and cosmic rays from deep space.This work focuses on developing a solution to protect against space radiation. Our proposal is inspired by the Earth's magnetosphere, aiming to replicate its protective features on a smaller scale. The technology could be tested on a CubeSat, with the goal of studying the effectiveness of this magnetic shielding system for future applications in space missions.

We propose a new model in which the fundamental physical constants, such as the speed of light and the gravitational constant, vary synchronously across the entire universe. This variation depends on the local gravitational field, leading to a classification of space into different "types" based on gravitational strength. These space types influence the manifestation of both quantum and classical laws. Our model offers a novel approach to unify quantum mechanics with classical physics and potentially explains phenomena such as dark matter, dark energy, quantum gravity, and the mass of neutrinos. Additionally, we discuss how this model aligns with the theory of relativity and accounts for phenomena like time dilation observed in GPS systems.

Quantum computing faces significant challenges due to quantum noise and gate errors, particularly in noisy intermediate-scale quantum [9] devices. Traditional error mitigation methods often fall short of achieving high circuit fidelity due to inherent system imperfections. This paper introduces Quantum-Classical Evolutionary Optimization [1], a novel hybrid framework that integrates quantum circuit mutation strategies with classical optimization techniques. QCEO adapts quantum circuits in real-time by treating quantum gates as evolutionary genes, iteratively optimizing them for improved noise resistance and fidelity. In experiments on both simulated environments and IBM Quantum hardware, QCEO demonstrates a 10-15% improvement in fidelity compared to traditional methods such as readout error correction and zero-noise extrapolation. Beyond fidelity improvement, QCEO’s ability to dynamically adapt to different noise profiles positions it as a versatile tool that can be integrated with emerging quantum algorithms like Variational Quantum Algorithms [4] and Quantum Approximate Optimization Algorithms [10]. This framework opens up new possibilities for advancing quantum computing in fields ranging from cryptography to quantum machine learning by ensuring higher performance in noisy quantum systems.

We investigate a coupled, non-linear dynamical systems model for the relationship between population and depleting resources inspired by limits to growth. The model is determined by logistic growth in population with carrying capacity determined by resources. The rate of decline of resources is determined linearly by the population. The model produces an initial exponential increase in population followed by a decrease to the fixed point while congruently resources decrease in a sigmoidal fashion to the fixed point. We fit the model to world population over the period 10000 BC to 2021 in different time intervals corresponding to different growth rates. We show a number of projections to 2500 based on fitting to the time period of 1950 to 2021 with various parameter constraints.